Jungle is the best role by far to carry with. To carry with it, you need to control the game by taking objectives, and making sure your lanes are all ahead.
Mid is second easiest, because they can easily positively influence their jungler, and negatively influence the enemy jungler.
The other two are FACTS, this one is my opinion. Top is 3rd best because you can easily snowball your lane. Almost all top laners in this meta can 1v1 well, and can easily force trades/fights. When you get ahead, you keep shoving and make people come to you. If they dont, free towers, and free kills. If they do, easy double kills (or your team gets tower if they know what they are doing)
As ADC, although you CAN carry, Its a lot harder because u need 2-3 items, depending on what carry you are playing. If your other lanes feed too hard before you can pop off, you will have a hard time.
And support... well you can't really carry on support. You can get your lanes ahead, but if they don't know how to play, there's nothing you can do.